Index formula for MacPherson cycles of affine algebraic varieties
Schürmann, Jörg ; Tibăr, Mihai
Tohoku Math. J. (2), Tome 62 (2010) no. 1, p. 29-44 / Harvested from Project Euclid
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We give explicit MacPherson cycles for the Chern-MacPherson class of a closed affine algebraic variety $X$ and for any constructible function $\alpha$ with respect to a complex algebraic Whitney stratification of $X$. ¶ We define generalized degrees of the global polar varieties and of the MacPherson cycles and we prove a global index formula for the Euler characteristic of $\alpha$. Whenever $\alpha$ is the Euler obstruction of $X$, this index formula specializes to the Seade-Tibăr-Verjovsky global counterpart of the Lê-Teissier formula for the local Euler obstruction.
Publié le : 2010-05-15
Classification:  Characteristic classes,  constructible function,  affine polar varieties,  Euler obstruction,  index theorem,  characteristic cycles,  stratified Morse theory,  14C25,  14C17,  14R25,  32S60,  14D06,  32S20 
@article{1270041025,
     author = {Sch\"urmann, J\"org and Tib\u ar, Mihai},
     title = {Index formula for MacPherson cycles of affine algebraic varieties},
     journal = {Tohoku Math. J. (2)},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 29-44},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270041025}
}

Schürmann, Jörg; Tibăr, Mihai. Index formula for MacPherson cycles of affine algebraic varieties. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp.  29-44. http://gdmltest.u-ga.fr/item/1270041025/